Nonlinear effects, such as self-phase modulation, cross-phase modulation and four-wave mixing, are known in optical transmission systems; in particular, in transmission systems which operate on the WDM principle (wavelength division multiplexing). These cause signal distortion in the optical signal to be transmitted in the optical fiber. Nonlinear effects such as these in an optical fiber can be described by the nonlinearity coefficient.
In order to determine the nonlinearity coefficient of an optical fiber, the publication by Y. Namihira, A. Miyata, N. Tanahashi, xe2x80x9cNonlinearity coefficient measurements for dispersion shifted fibres using self-phase modulation method at 1.55 xcexcmxe2x80x9d, Electronic Letters, 1994, Vol. 30, No. 14, pages 1171-1172, for example, discloses a measurement arrangement in which the nonlinearity characteristics of an optical fiber are determined by using the self-phase modulation method. Measurement methods such as these are dependent on access to the start and end of the optical fibers to be measured, although this involves considerable measurement effort and is virtually impossible in already existing optical communications networks; that is to say, in optical fibers which have already been laid. In addition, a separate return channel is required from the fiber end to the fiber start in order to transmit the measured information.
An object to which the present invention is directed is to improve the determination of the nonlinearities in an optical fiber, and to allow the nonlinearities of an optical fiber to be measured at one end; that is to say, at the start or at the end of the optical fiber.
A major aspect of the measurement method according to the present invention is that, in a first step, at least one optical test signal is injected into the optical fiber, whose test signal power is varied, and a first onset threshold for the stimulated Brillouin scatter is determined on the basis of the change in power of the backscattered optical signal. Furthermore, in a second step, in addition to the optical test signal, at least one modulated optical pump signal is injected with a predetermined pump signal power and at a first pump wavelength into the optical fiber, and a second onset threshold for the stimulated Brillouin scatter is determined on the basis of the change in the optical test signal power. Finally, the nonlinearity coefficient of the optical fiber is determined by evaluation of at least the first and the second onset threshold, of the test and pump signal parameters, and the fiber parameters. It is particularly advantageous that the measurement method according to the present invention makes it possible to determine the nonlinearity coefficient via a measurement at only one end; that is to say, at the receiving end or transmitting end. This is an enormous advantage, particularly for the determination of the fiber nonlinearities of optical fibers which have already been laid.
In a second embodiment of the measurement method for determining the nonlinearities in an optical fiber, in a first step, at least one optical test signal is injected with a test signal power and at a test signal wavelength into the optical fiber, and the power of the backscattered optical signal is measured, and a first ratio is formed from the injected test signal power and the power of the backscattered optical signal. Furthermore, in a second step, in addition to the optical test signal which has a test signal power and is at a test wavelength, at least one modulated optical pump signal is injected with an adjustable pump signal power and at a first pump wavelength into the optical fiber, and the power of the backscattered optical signal is measured, and a second ratio is determined from the injected test signal power and the power of the backscattered optical signal. Here, the adjustable pump signal power of the modulated optical pump signal is increased or decreased until the second ratio matches the first ratio. In this case, the nonlinearity coefficient of the optical fiber is then determined by evaluation of the test and pump signal parameters as well as the fiber parameter. The variation according to the present invention of the pump signal power of the modulated optical pump signal alternatively makes it possible to determine the nonlinearity coefficient of the optical fiber by ratio formation, evaluating the observed fiber parameters and trial parameters.
A further advantage of the measurement method according to the present invention is that the test and pump signal parameters which are evaluated on the basis of the first variant of the measurement method according to the present invention are the test signal wavelength, the predetermined pump signal power, the first pump wavelength and the modulation frequency of the optical pump signal. Furthermore, the test signal power, the test signal wavelength, the pump signal power that is set, the first pump wavelength, and the modulation frequency of the optical pump signal are evaluated as the test and pump signal parameters; crucial for the second embodiment of the measurement method according to the present invention.
Theoretical principles relating to the measurement method according to the present invention for determination of the nonlinearities and the dispersion in an optical fiber will be explained in the following text.
In optical fibers, the nonlinear effect of xe2x80x9cstimulated Brillouin scattering (SBS)xe2x80x9d occurs as a function of the injected power of an optical test signal or signal. This narrowband SBS effect with a line width of xcex94xcexdB≈25 MHz, which is governed by the phonon life is known (in this context, see Govind P. Algrawal xe2x80x9cNonlinear Fiber Opticsxe2x80x9d, Academic Press, 1995, pages 370 to 375). Furthermore, U.S. Patent Specification U.S. Pat. No. 3,705,992 disclosed the onset threshold for SBS being increased in proportion to the ratio of the spectral width xcex94xcexds of the optical signal which is injected into the optical fiber to the line width xcex94xcexdB; that is to say,
ISBSxcx9cxcex94xcexds/xcex94xcexdB
where ISBS=intensity of the injected optical signal at the SBS onset threshold
In this case, the governing factor for reaching the SBS onset threshold is the energy which is spectrally integrated in a frequency separation of width xcex94xcexdB. In standard monomode fibers, the SBS onset threshold occurs, for example, at slightly below 10 mW for unmodulated optical signals or test signals, and at a level which is higher by a factor of 2 to 3 dB for binary amplitude-modulated optical signals. The increase for binary amplitude-modulated optical signals is due to the fact that the optical signal power is shared between modulation sidebands and the carrier signal and, particularly at data rates in the Gbit/s range, the power of the data signal is distributed over a broad spectral band.
In the case of amplitude-modulated signals, SBS leads to signal distortion due to overmodulation (see, in particular, H. Kawakani, xe2x80x9cOvermodulation of Intensity modulated Signals due to stimulated Brillouin scatteringxe2x80x9d, Electronic Letters, Volume 30, No. 18, pages 1507 to 1508), since the carrier of the amplitude-modulated optical signal, in which the spectral energy density for chip-free modulation is identical to the laser light source, essentially experiences severe additional attenuation due to the SBS.
The SBS onset threshold can be increased considerably by considerably reducing the spectral energy density of the optical signal, integrated over a frequency band of width xcex94xcexdB. Thus, in the case of amplitude-modulated optical signals, the carrier signal power, measured with a resolution of xcex94xcexdB, should be reduced to values which are considerably below the SBS threshold power. A reduction such as this can be achieved by frequency modulation or phase modulation.
The SBS effects in the optical fiber occur essentially within the first 20 km (effective length Leff) in a standard monomode fiber. In this case, the optical signal requires the following time:   τ  =                              L          eff                ·        n            c        ⁢          (              =                              0.1            ⁢                          xe2x80x83                        ⁢            ms            ⁢                          xe2x80x83                        ⁢            for            ⁢                          xe2x80x83                        ⁢                          L              eff                                =                      20            ⁢                          xe2x80x83                        ⁢            km                              )      
to pass through the effective length Leff. In order to reduce SBS effects, the optical injected power per frequency separation xcex94xcexdB, averaged over a time interval, should be very much less than the time xcfx84 spent below the SBS threshold power. This requirement makes it possible to derive the necessary relationship between the modulation shift and the modulation frequency for various forms of modulation, for SBS suppression via frequency modulation and amplitude modulation.
In order to reduce the spectrally narrow carrier line of the optical signal and to uniformly distribute its power over as many lines, which are newly created by the phase modulation, as possible, with a frequency interval of more than xcex94xcexdB, the phase modulation should be carried out using modulation frequencies greater than xcex94xcexdB. As the phase shift increases,             that      ⁢              xe2x80x83            ⁢      is      ⁢              xe2x80x83            ⁢      to      ⁢              xe2x80x83            ⁢      say      ⁢              xe2x80x83            ⁢      the      ⁢              xe2x80x83            ⁢      modulation      ⁢              xe2x80x83            ⁢      index      ⁢              xe2x80x83            ⁢      m        =                  Δ        ⁢                  xe2x80x83                ⁢                  f          p                            f        m                                                                    where              ⁢                              xe2x80x83                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢                              f                p                                      =                          peak              ⁢                              xe2x80x83                            ⁢              frequency              ⁢                              xe2x80x83                            ⁢              error                                ;                                                                        f              m                        =                          modulation              ⁢                              xe2x80x83                            ⁢              frequency                                ;                    
the spectral power per frequency separation decreases. Such amplitude modulation in the optical fiber can be produced, for example, by the nonlinear effect of cross-phase modulation (XPM) via the additional injection of highly amplitude-modulated pump signals in addition to the optical signals. In this case, the phase modulation produced by cross-phase modulation (XPM) has an RC low-pass filter response along the optical fiber. The cut-off frequency xcfx89g of the xe2x80x9clow-pass filter responsexe2x80x9d decreases linearly as the channel separation increases, owing the dispersion-dependent slip in the WDM transmission channels. In order to achieve effective phase modulation over a broad wavelength band via XPM, it is necessary to choose the magnitude of the modulation frequency to be as low as possible, although this should never be below the line width xcex94xcexdB.
The intensity ISBS of the backscattered optical signal due to SBS at the fiber start increases in the backward direction as the injected optical signal power increases in accordance with the following exponential relationship; in this context, see Govind P. Algrawal xe2x80x9cNonlinear Fiber Opticsxe2x80x9d, 1995, Section 9.2.1:                                           I            SBS                    ⁡                      (            0            )                          =                                            I              SBS                        ⁡                          (              z              )                                *                      exp            ⁡                          (                                                                    g                    B                                    *                                      I                    S                                    *                                      L                    eff                                                  -                                  α                  *                  z                                            )                                                          (                  A          ⁢                      -                    ⁢          1                )                                          L          eff                =                              1                          α              *                                ⁢                      (                          1              -                              exp                ⁡                                  (                                                            -                      α                                        *                    z                                    )                                                      )                                              (                  A          ⁢                      -                    ⁢          2                )            
where
If the amplitude-modulated optical pump signal which produces the XPM and the optical signal propagate simultaneously in the fiber, the optical signal is increasingly phase-modulated on the basis of the XPM as the path length increases. By way of example, phase modulation with a phase shift of 1.435 rad distributes the spectral power of the carrier signal over a number of frequencies in this case; that is to say, for example, uniformly between the carrier wave and the two first sidebands. If the modulation frequency is, in this case, greater than the SBS line width xcex94xcexdB, then only just ⅓ of the spectral energy density is available to form the SBS, for example; that is to say, the SBS onset threshold is increased by a factor of 3 from the point at which such a phase shift is reached by the XPM. The local SBS onset threshold thus can be calculated as a function of the characteristics of the injected modulated pump signal and of the optical fiber, as well as of the injected optical signal, and the SBS onset threshold which results from this and is dependent on the optical pump signal can be determined for the entire fiber.
The SBS onset threshold in the presence of the optical pump signal can be calculated by breaking down the fiber into small part sections in conjunction with equation (A-1). To a first approximation, the fiber is initially broken down into n=2 part sections, from which it follows using equations (A-1) and (A-2) for a fiber of length Z/2 that:
ISBS(z/2)=ISBS(z)*exp(gB*Is*exp(xe2x88x92xcex1*z/2)*1/xcex1*(1xe2x88x92exp(xe2x88x92xcex1*z/2))xe2x88x92xcex1z/2)xe2x80x83xe2x80x83(A-3)
and
ISBS(0)=ISBS(z/2)*exp(gB*Is*1/xcex1*(1xe2x88x92exp(xe2x88x92xcex1*z/2))xe2x88x92xcex1z/2)xe2x80x83xe2x80x83(A-4)
If the path is broken down into n path sections:                                           I            SBS                    ⁡                      (            0            )                          =                                            I              SBS                        ⁡                          (              z              )                                *          exp          ⁢                      xe2x80x83                    ⁢                                    "AutoLeftMatch"              "AutoRightMatch"                        [                                          g                B                            *                              I                S                            *                              xe2x80x83                            ⁢                              "AutoLeftMatch"                                                                            {                                              1                        +                                                                              ∑                                                          k                              =                              1                                                                                      n                              -                              1                                                                                ⁢                                                      exp                            ⁡                                                          (                                                                                                -                                  α                                                                *                                                                  k                                  /                                  n                                                                *                                z                                                            )                                                                                                                          }                                        *                                          1                      /                      α                                        *                                          (                                              1                        -                                                  exp                          ⁡                                                      (                                                                                          -                                α                                                            *                              z                                                        )                                                                                              )                                                        -                                      xe2x80x83                                    ⁢                                      "AutoLeftMatch"                                          α                      ⁢                                              xe2x80x83                                            ⁢                      z                                        ]                                                                                                          (                  A          ⁢                      -                    ⁢          5                )            
The following text considers the 2nd path section, equation (A-3). Taking account of the spectral change in the optical signal Is resulting from the XPM which is induced by a sinusoidally amplitude-modulated optical pump signal Ip, in the fiber, this results in addition to the path attenuation exp(xe2x88x92xcex1*z/2) in a further additional attenuation for the carrier by the attenuation factor:
J02(m)=J02("xgr"*xcex3*Ip*1/xcex1*(1xe2x88x92exp(xe2x88x92xcex1*z/2)),xe2x80x83xe2x80x83(A-6)
where m is the phase shift or modulation index caused by the XPM on the first path section of length z/2, and "xgr" is a polarization-dependent constant. For randomly varying polarization: "xgr"=8/9
Investigations have shown that the carrier of the amplitude-modulated optical pump signal (that is to say J02(m)) is substantially included in the change in the intensity of the backscattered optical signal. From this, it follows for equation (A-3) with (A-6):
ISBS(z/2)=ISBS(z)*exp[gB*Is*1/xcex1*(1xe2x88x92exp(xe2x88x92xcex1*z/2))*exp(xe2x88x92xcex1*z/2)*J02(m(z/2))xe2x88x92xcex1z/2)xe2x80x83xe2x80x83(A-7)
where
m(x)="xgr"*xcex3*Ip*1/xcex1*(1xe2x88x92exp (xe2x88x92xcex1*x))xe2x80x83xe2x80x83(A-8)
Substituting equation (A-7) in equation (A-4) gives the intensity of the backscattered optical signal ISBS, with approximate consideration of the XPM.
ISBS(0)=ISBS(z)*exp 
[gB*Is*exp(xe2x88x92xcex1*z/2)*J02
(m(z/2))*1/xcex1** 
(1xe2x88x92exp(xe2x88x92xcex1*z/2))*1/xcex1*(1
xe2x88x92exp(xe2x88x92xcex1*z/2))xe2x88x92xcex1z/2]
**exp[gB*Is*1/xcex1*(1
xe2x88x92exp(xe2x88x92xcex1*z/2))xe2x88x92xcex1z/2)=
=ISBS(z)*exp[gB*Is*1/xcex1*(1
xe2x88x92exp(xe2x88x92xcex1*z/2))**{1
+exp(xe2x88x92xcex1*z/2)*J02(m
(z/2)))}xe2x88x92xcex1z]
In order to improve the accuracy, the fiber is broken down into n subelements (equation A-5)), thus, by an analogous procedure, resulting in:                                           I            SBS                    ⁡                      (            0            )                          =                                            I              SBS                        ⁡                          (              z              )                                *                      exp            ⁡                          [                                                                    g                    B                                    *                                      I                    S                                    *                                      1                    /                    α                                    *                                      (                                          1                      -                                              exp                        ⁡                                                  (                                                                                    -                              α                                                        *                                                          z                              /                              n                                                                                )                                                                                      )                                    *                                      {                                          1                      +                                                                        ∑                                                      k                            =                            1                                                                                n                            -                            1                                                                          ⁢                                                                              exp                            ⁡                                                          (                                                                                                -                                  α                                                                *                                                                  k                                  /                                  n                                                                *                                z                                                            )                                                                                *                                                                                    J                              0                              2                                                        ⁡                                                          (                                                              m                                ⁡                                                                  (                                                                      k                                    *                                                                          z                                      /                                      n                                                                                                        )                                                                                            )                                                                                                                                            }                                                  -                                  α                  ⁢                                      xe2x80x83                                    ⁢                  z                                            ]                                                          (                  A          ⁢                      -                    ⁢          9                )            
Comparison of equation (A-9) with equation (A-1) shows that
Leff=1/xcex1*(1xe2x88x92exp (xe2x88x92xcex1*z))
can be replaced by the expression                                           L            eff                    ⁡                      (                          z              ,              α              ,              γ              ,                              I                p                                      )                          =                              1            /            α                    *                      (                          1              -                              exp                ⁡                                  (                                                            -                      α                                        *                                          z                      /                      n                                                        )                                                      )                    *                      {                          1              +                                                ∑                                      k                    =                    1                                                        n                    -                    1                                                  ⁢                                                      exp                    ⁡                                          (                                                                        -                          α                                                *                                                  k                          /                          n                                                *                        z                                            )                                                        *                                                            J                      0                      2                                        ⁡                                          (                                              m                        ⁡                                                  (                                                      kz                            /                            n                                                    )                                                                    )                                                                                            }                                              (                  A          ⁢                      -                    ⁢          10                )            
The effective length Leff is thus, according to equation (A-10) and (A-8), dependent on the nonlinearity coefficient xcex3 of the optical fiber, and on the optical power of the amplitude-modulated optical pump signal Ip.
If there is a wide frequency separation between the optical pump signal and the injected optical test signal or signals, this results, especially due to the dispersion-dependent slip between the optical signal and the optical pump signal, which occurs in a standard monomode fiber (SSMF), in further dependencies between the effective length Leff and the fiber dispersion, the frequency separation (wavelength separation) of the optical pump signal and optical test signal, and the modulation frequency of the optical pump signal.
From equation (A-10), this results in the following expression for Leff(z,xcex1,xcex3,Ip) for a power section z consisting of n subelements:                                           L            eff                    ⁡                      (                          z              ,              α              ,              γ              ,                              I                p                            ,              D              ,                              Δ                ⁢                                  xe2x80x83                                ⁢                λ                            ,                              f                ⁢                                  xe2x80x83                                ⁢                mod                                      )                          =                              1            /            α                    *                      (                          1              -                              exp                ⁡                                  (                                                            -                      α                                        *                                          z                      /                      n                                                        )                                                      )                    *                      {                          1              +                                                ∑                                      k                    =                    1                                                        n                    -                    1                                                  ⁢                                                      exp                    ⁡                                          (                                                                        -                          α                                                *                                                  k                          /                          n                                                *                        z                                            )                                                        *                                                            J                      0                      2                                        ⁡                                          (                                                                        m                          ⁡                                                      (                                                          kz                              /                              n                                                        )                                                                          *                                                  Le                          ⁡                                                      (                                                                                          k                                *                                                                  z                                  /                                  n                                                                                            ,                              α                              ,                              D                              ,                                                              Δ                                ⁢                                                                  xe2x80x83                                                                ⁢                                λ                                                            ,                                                              f                                ⁢                                                                  xe2x80x83                                                                ⁢                                mod                                                                                      )                                                                                              )                                                                                            }                                              (                  A          ⁢                      -                    ⁢          11                )            
where       Le    ⁡          (                        k          *                      z            /            n                          ,        α        ,        D        ,                  Δ          ⁢                      xe2x80x83                    ⁢          λ                ,                  f          ⁢                      xe2x80x83                    ⁢          mod                    )        ≈            (                        1          +                      exp            ⁡                          (                                                -                  2                                *                L                *                α                            )                                -                      2            *                          exp              ⁡                              (                                                      -                    L                                    *                  α                                )                                      *                          cos              ⁡                              (                                  L                  *                  β                  *                  ω                                )                                                                          α            2                    +                                    β              2                        *                          ω              2                                          )              1      2      
where:
L=k*z/n,
xcex2=D*xcex94xcex,
xcfx89=2*xcfx80*fmod;
m(kz/n)="xgr"*xcex3*Ip*Le;
Le(k*z/n,xcex1,D,xcex94xcex,fmod) describes the variation of the modulation index {m(kz/n)} interalia also as a function of the modulation frequency and of the wavelength separation between the optical pump signal and the test signal.
For high dispersion values D, high modulation frequencies fmod and wide wavelength separation xcex94xcex, Leff once again assumes its original form from equation (A-2); that is to say, Leff is dependent only on the fiber attenuation xcex1 and the location z, and the SBS suppression caused by the optical pump signal is reduced.
The variation in the SBS onset threshold as a function of the pump, signal and fiber parameters is obtained by substitution of equation (A-10) or equation (A-11) in:
xe2x80x83PSBS=21*Aeff/gB/Leffxe2x80x83xe2x80x83(A-12)
from Godvind P. Agrawal, xe2x80x9cNonlinear Fiber Opticsxe2x80x9d, Academic Press, 1995, formula (9.2.6).
The dispersion D and the nonlinearity coefficient y can be determined from equation (A-11) and equation (A-12) from the variation in the effective length Leff(z,xcex1,Ip,D,xcex94xcex,fmod) as a function of the optical pump power Ip, of the wavelength difference between the pump signal and the test signal xcex94xcex, as well as the modulation frequency fmod and the SBS onset threshold PSBS.
Based on the measurement method according to the present invention, the nonlinearity coefficient xcex3 and the dispersion D are determined using the shift in the SBS onset threshold PSBS resulting from the change in the spectrum of the injected optical test signal, which is caused by the cross-phase modulation (XPM) resulting from the sinusoidally amplitude-modulated optical pump signal in the optical fiber, using equation (A-12).
In this case, the Brillouin gain constant gB and the effective area Aeff are optical fiber constants, which are naturally available for the optical fiber to be measured, or can be determined without any significant technical effort. However, as already mentioned, the effective length Leff(z,xcex1,Ip,D,xcex94xcex,fmod) can be influenced by the trial conditions and, based on formula (A-11), depends on the length of the fiber z, on the fiber attenuation xcex1, on the wavelength difference between the optical pump signal and test signal xcex94xcex and the modulation frequency fmod of the amplitude-modulated optical pump signal.
In the measurement method according to the present invention for determination of the nonlinearity coefficient xcex3 of an optical fiber, if the wavelength difference between the optical pump signal and the test signal xcex94xcex is, for example, less than 1 nm, and the modulation frequency fmod of the amplitude-modulated optical pump signal is less than 200 MHz, the effect of the dispersion influence on the measurement result can be ignored; that is to say, the effective length Leff does not depend, to a first approximation, on the fiber dispersion D. According to the present invention, a first SBS onset threshold PSBS1 and a second SBS onset threshold PSBS2, which is shifted owing to the cross-phase modulation (XPM) caused by the injected modulated pump signal in the optical fiber, are measured, and these are evaluated together with the test and pump signal parameters as well as the fiber parameters using equations (A-11) and (A-12), with the dispersion D being negligible. Alternatively, according to the present invention, a first measurement and a second measurement of the backscattered optical power can be carried out, with only the optical test signal being injected into the optical fiber for the first measurement, with a predetermined power and at a predetermined wavelength, and with the modulated optical pump signal in addition to the optical test signal being injected into the optical fiber for the second measurement, in order to produce the cross-phase modulation (XPM). In this case, in both the first measurement and the second measurement, the injected power of the optical test signal is increased until a predetermined ratio is obtained between the injected power of the optical test signal and the backscattered power. The optical test signal and optical pump signal powers used for the first and second measurements in the measurement method, together with the test and pump signal parameters as well as the fiber parameters, are once again evaluated using equations (A-11) and (A-12), with the dispersion D being negligible.
If, in addition to determination of the nonlinearity coefficient xcex3, it is also intended to determine the dispersion constant D of an optical fiber using the measurement method according to the present invention, then the wavelength difference between the optical pump signal and the test signal xcex94xcex is chosen, by way of example, to be greater than 10 nm; that is to say, the effective length Leff depends on the fiber dispersion D and the wavelength difference between the optical pump signal and test signal xcex94xcex. Based on the measurement method according to the present invention, in addition to the first SBS onset threshold PSBS1, without any injected modulated optical pump signal, a third SBS onset threshold PSBS3 is determined which has a different profile from the second SBS onset threshold PSBS2 owing to the change to the pump signal parameters, or a third measurement is carried out in which, in addition to the optical test signal, the changed modulated optical pump signal is injected into the optical fiber in order to produce the cross-phase modulation (XPM) is used to increase the injected power in the optical test signal until a predetermined ratio is reached between the injected power in the optical test signal and the backscattered power. The detailed procedure of the measurement method according to the present invention and the determination of the nonlinearity constant xcex3 and of the dispersion constant D will be explained in more detail with reference to the following exemplary embodiment.